leadTermValuation -- The valuation defined by leading terms

• Usage:

  v = leadTermValuation R

• Inputs:
  • R, a polynomial ring, the ring whose term order is used to define the valuation
• Outputs:
  • v, an instance of the type Valuation, the lead term valuation

i1 : R = QQ[a,b,c, MonomialOrder => Lex];

i2 : v = leadTermValuation R;

i3 : f = 13*a^2*b + a*c^3;

i4 : g = 5*a^2*c + b^3;

i5 : v f

o5 = | -2 |
     | -1 |
     |  0 |

o5 : Ordered QQ^3 module

i6 : v g

o6 = | -2 |
     |  0 |
     | -1 |

o6 : Ordered QQ^3 module

i7 : v f < v g

o7 = true